Basic Math Examples

$\frac{\sqrt{5} \cdot \sqrt{15}}{\sqrt{3}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{3}$ into a single radical.

$\sqrt{5} \cdot \sqrt{\frac{15}{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt{5 \cdot \frac{15}{3}}$

Step 3

Combine $5$ and $\frac{15}{3}$ .

$\sqrt{\frac{5 \cdot 15}{3}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{5 \cdot 15}{3}$ by cancelling the common factors.

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Step 4.1.1

Factor $3$ out of $5 \cdot 15$ .

$\sqrt{\frac{3 (5 \cdot 5)}{3}}$

Step 4.1.2

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (5 \cdot 5)}{3 (1)}}$

Step 4.1.3

Cancel the common factor.

$\sqrt{\frac{3 (5 \cdot 5)}{3 \cdot 1}}$

Step 4.1.4

Rewrite the expression.

$\sqrt{\frac{5 \cdot 5}{1}}$

Step 4.2

Divide $5 \cdot 5$ by $1$ .

$\sqrt{5 \cdot 5}$

Step 5

Multiply $5$ by $5$ .

$\sqrt{25}$

Step 6

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$5$